Method for linearsing high-frequency amplifier

ABSTRACT

A predistorter is connected upstream of a high-frequency amplifier to be linearized. A predistortion factor is adaptively modified in the predistorter in such a way as to compensate non-linearities of the amplifier as well as possible. The quotient of the output signal of the high-frequency amplifier and the input signal of the predistorter is produced first. An average amplification is then determined based on the signal quotient. A correction term is produced for the predistortion factor, this correction term being dependent on the extent of the deviation of the average amplification from a set value. The predistortion factor is adaptively modified in such a way as to minimize the correction term.

PRIOR ART

The present invention concerns a method for linearization of ahigh-frequency amplifier, to which a predistorter is connected upline inwhich a predistortion factor is altered adaptively so that a linearrelation exists between the output signal of the high-frequencyamplifier and the input signal of the predistorter.

The transmission behavior of a high-frequency amplifier is highlydependent on its rest current (bias voltage). The higher the biascurrent, the better the linearity of the amplifier in general. However,the power consumption of the amplifier increases and the efficiencydiminishes with the closed-circuit current. This can lead to asignificant cost in power supply, cooling, etc., especially inhigh-frequency power amplifiers. If high linearity of the amplifier isdispensed with, this can be operated with a lower closed-circuit currentso that the cost of power supply and cooling of the amplifier isreduced. Operation of the amplifier in its linear control range can beomitted if a predistorter that largely compensates for the distortionsof the amplifier is connected upline of the amplifier. Predistorters forhigh-frequency amplifiers are known from the literature, for example,IEEE Transactions on Communications, Vol. 45, No. 10, October 1997, pp.1167-1171. The adaptive digital predistorter described in this articleoperates as follows. The amount of the signal to be predistorted ismultiplied by a real value and a real value added to the phase in orderto balance the nonlinear effects of the amplifier. The correspondingvalues for amount and phase are read from a-table whose address isdetermined from the amplitude of the signal being predistorted. Theamount and phase are adapted separately. The correction value to controladjustment of the amount is the difference in amounts of thepreamplifier output signal and the signal being predistorted. Thecorrection value for phase adjustment is the difference in phases of theamplifier output signal and the signal being predistorted.

The task underlying the invention is to provide a method of the typejust mentioned with which the best possible linearization of ahigh-frequency amplifier can be achieved.

Advantages of the Invention

The stated task is solved by the features of claim 1, in that thequotient of the output signal of the high-frequency amplifier and theinput signal of the predistorter is initially formed and an averageamplification then determined from the signal quotient. A correctionterm is formed for a predistortion factor formed in the predistorterthat depends on the deviation of the average amplification relative to areference value. Finally, the predistortion factor is altered adaptivelyso that the correction term becomes minimal. According to the invention,the amount and phase of the signal need not be calculated, as in thecited prior art, but instead the quotient of the formed signal, so thatthe correction term for adjustment can be determined with limitedcalculation cost.

Since the characteristic of the predistorter is adaptively set with thismethod, temperature- and aging-dependent amplification changes can alsobe compensated. An automatic adjustment of the predistorter duringoperation also makes adjustment of the predistorter during manufactureunnecessary.

Advantageous modifications of the invention are apparent from thesubclaims. A particular good convergence during adjustment of thepredistorter is obtained by the fact that the correction term for thepredistortion factor is formed from the product of an adjustmentconstant and the difference between the inverse average amplificationand 1.

It is expedient that the power or a quantity derived from it be formedfrom the input signal of the predistorter, that the power or thequantity derived from it then be linearly quantized, that a value of thepredistortion factor be assigned to each possible quantization step,that an average amplification be determined for each quantization step,and that for each distortion factor allocated to a quantization step acorrection term dependent on the average amplification determined at thecorresponding quantization step be formed, which is minimized byadaptive variation of the predistortion factor. The averageamplification of each quantization step is advantageously determined bythe fact that amplification values are formed over a specified timeinterval from the time- and value-discrete scanning values of the outputsignal of the high-frequency amplifier and the input signal of thepredistorter, that all amplification values corresponding to acorresponding quantization step are accumulated, and that for eachquantization step the amplification value resulting at the end of thetime interval from accumulation is divided by the number of accumulationsteps.

The adjustment constants preferably have a value dependent on thecorresponding quantization step to which the predistortion factor isassigned.

An optimal adjustment rate for the predistortion factor can be achievedby the fact that the smaller of two values is chosen as adjustmentconstant, in which the one value is 0.5 and the other value depends onthe number of accumulations of amplification values in the correspondingquantization step.

BRIEF DESCRIPTION OF THE DRAWINGS

The only FIGURE in the drawing is of a high frequency power amplifierVV—hereafter called amplifier—and a predistorter PD connected upline.

DETAILED DESCRIPTION

The input signal of the predistorter is denoted x(t), the output signalof the predistorter PD is denoted y(t), which is fed to the input of theamplifier VV, and the output signal of the amplifier VV is denoted z(t).The input signal x(t) and therefore also the two other signals y(t) andz(t) are fully analytical, i.e., they have a real and an imaginary part.The input signal x(t) can be a base band signal or a signal in theintermediate or high-frequency range. A quadrature mixer is ordinarilyused for transformation of the quadrature component of a base bandsignal into the intermediate or high-frequency range. If a signal x(t)that also has quadrature components is present in the intermediatefrequency range or high frequency range, the depicted arrangement of apredistorter PD and an amplifier VV can also be used in the intermediateand high frequency range. However, if a signal x(t) that has only a realpart is present in the intermediate or high-frequency range, the missingimaginary part can also be recovered from the real part of the signal bymeans of a Hilbert filter that carries out essentially only a 90° phaseshift. In the following explanation of the circuit an input signal x(t)in the base band is assumed.

The relation between the input signal y(t) of the amplifier VV and itsoutput signal z(t) can be represented according to equation (1).

z(t)=gVV(Ay(t))·y(t)  (1)

Here, Ay(t)=|y(t)|.gVV(Ay(t)) is a complex amplification factor thatdepends only on the amplitude Ay(t) of the complex input signal y(t). Ifthe input signal y(t) is broken down into amount and phase, one obtainsfor the output signal z(t) according to equation (2):

 z(t)=fAM,VV(Ay(t))·e ^((fPM,VV(AY(t))+Φy(t)))  (2)

The amplitude Az(t) and the phase Φz(t) of the complex output signalz(t), according to equations (3) and (4), are then:

Az(t)=fAM,VV(Ay(t))  (3)

Φz(t)=fPM,VV(Ay(t))+Φy(t)  (4)

In equations (2), (3) and (4), fAM,VV denotes an amplitude-amplitudeconversion and fPM,VV denotes an amplitude-phase conversion that aregenerated in undesired fashion by the amplifier VV. A comparison ofequation (1) with equation (2) yields the amplification factor accordingto equation (5). $\begin{matrix}{{{gVV}\left( {{Ay}(t)} \right)} = {\frac{{fAM},{{VV}\left( {{Ay}(t)} \right.}}{{Ay}(t)} \cdot ^{{\quad {fPM}},{{VV}{({{Ay}{(t)}})}}}}} & (5)\end{matrix}$

The predistorter PD is a nonlinear element, like amplifier VV. Apredistortion factor gPD generated by the predistorter is to be set sothat it compensates for the nonlinearity of the amplification factor gVVof the following amplifier VV. The relationship between the input signalx(t) and the output signal y(t) of the predistorter PD is represented inequation (6).

y(t)=gPD(Ax(t))·x(t)  (6)

The predistortion factor gPD is dependent only on the amplitude Ax(t) ofthe complex input signal x(t). As can be gathered in the circuit shownin the FIGURE, the output signal y(t) of the predistorter PD developsowing to the fact that a multiplier M multiplies the input signal x(t)by the predistortion factor gPD. The amplitude Ay(t) and the phase Φy(t)of the complex output signal y(t) of the predistorter PD can bedescribed according to equations (7) and (8).

Ay(t)=fAM,PD(Ax(t))  (7)

Φy(t)=fPM,PD(Ax(t))+Φx(t)  (8)

In equations (7) and (8), fAM,PD denotes the amplitude-amplitudeconversion and fPM,PD the amplitude-phase conversion of the predistorterPD. If equations (7) and (8) are introduced into equations (3) and (4),the relations shown in equations (9) and (10) between theamplitude-amplitude and amplitude-phase conversions in the amplifier VVand the predistorter PD are obtained under the secondary condition ofperfect linearization, i.e., Az(t)=Ax(t) and Φz(t)=Φx(t).

 fAM,PD(Ax(t))=f ¹ AM,VV(Ax(t))  (9)

fPM,PD(Ax(t))=−fPM,VV(f ¹ AM,VV(Ax(t))  (10)

In equations (9) and (10), which verify how the predistorter PD is to bemodeled so that nonlinearity of the amplifier VV is compensated, f¹means the inverse function of f. Linearization of the amplifier VV istherefore only possible in the invertibly clear regions of theamplification characteristic. fAM,PD is therefore also invertiblyunique.

As shown by the block diagram of the predistorter PD depicted in theFIGURE, the two quadrature components of the input signal x(t) aresquared and added in a first functional block P, so that the powersPx(t) of the input signal x(t) lie at the output. Px(t)=|x(t)|²therefore applies. In the next functional block L, the power Px(t) isclearly imaged in another quantity Lx(t). The other quantity Lx(t) canbe logPx(t), for example. The power Px(t), however, need not beconverted into a new quantity Lx(t), but can be fed directly to a nextfunctional block Q. In this functional block Q, the input quantity Lx(t)or directly the power Px(t) is linearly quantized. In the subsequentfunctional block A, in which adjustment of the predistortion factor gPDoccurs, a value of the predistortion factor gPD is placed in the tablepreferably at each quantization step. The dependence of thepredistortion factor on the quantization step is expressed hereafter bygPD(K(t)). The quantization steps K(t) then represent the addresses ofthe table in which the predistortion factors gPD(K(t)) are placed.

The functional block A contains the table with the predistortion factorgPD(K(t)) and carries out their adjustment. For this purpose, the inputsignal x(t) of the predistorter PD, on the one hand, and the outputsignal z(t) of the amplifier VV, on the other, are fed to the functionalblock A. The output signal z(t) of amplifier VV is picked up by ameasurement receiver MV whose task is essentially to transform theoutput signal z(t) of the amplifier VV back into the frequency positionin which the predistorter is implemented. It is assumed here that themeasurement receiver MV can be considered ideal. This means that it issupposed to produce much less distortion than the amplifier VV, which iseasy to fulfill because of the much smaller signal level of themeasurement receiver MV. The functional block A initially forms thequotient from the output signal z(t) of the amplifier VV and the inputsignal x(t) of the predistorter PD. The two signals x(t) and z(t) arepresent as time- and value-discrete scanning values, for which reasonthey are written hereafter as x(n) and z(n). n denotes the consecutiveindex for the scanning values within a stipulated time. The quotientz(n)/x(n) is then the instantaneous amplification at the scanning time nof the arrangement consisting of the predistorter PD and the amplifierVV.

As shown in equation (11), the amplification values placed in a tableaddressable by the quantization steps K are determined over thestipulated time interval of the input signal x(n) for each of thequantization steps K, in which the signal quotients z(n)/x(n) pertainingto the same quantization steps are accumulated. $\begin{matrix}{{V(K)} = {{V(K)} + \frac{z(n)}{x(n)}}} & (11)\end{matrix}$

In equation (12) the number of accumulations for each quantization stepK is counted; one can also speak of a hit frequency T(K) for eachquantization step K.

T(K)=T(K)+1  (12)

If, as shown in equation (13), the amplification value V(K) present atthe end of the stipulated time interval is divided by the hit frequencyT(K), the average amplification W(K) is obtained at the end of the timeinterval for the corresponding quantization step K. $\begin{matrix}{{W(K)} = \frac{V(K)}{T(K)}} & (13)\end{matrix}$

Let gPDm(K) be the predistortion factor for the K^(th) quantization stepin the m^(th) time interval. Wm(K) is the average amplification for theK^(th) quantization step calculated in the m^(th) time interval.

The deviation of the average amplification W(K) from a reference valueis used as correction value in order to adapt the predistortion factorgPD(K) until the correction value becomes minimal. If by adjustment ofthe predistortion factor gPD(K), the correction value ideally becomes 0,the nonlinearity of the amplification factor gVV(K) is fullycompensated. Good convergence during adjustment of the predistortionfactor gPD(K) to a value that guarantees high linearity of the overallarrangement is achieved with the adjustment equation (14).

gPDm+1(K)=gPDm(K)[1+Δ(K)(W ⁻¹ m(K)−1)  (14)

This adjustment equation (14) states that the predistortion factorgPDm+1 (K) for the current time interval m+1 follows from thepredistortion factor gPDm(K) of the preceding time interval m, on whicha correction value gPD(K)·Δ(K)(W⁻¹m(K)−1) is superimposed. In thecorrection term, Δ(K) is an adjustment constant dependent on thequantization step K. The correction term is also determined by thedeviation of the average amplification from a reference value. Inparticular, as can be gathered from equation (14), the correction valueis dependent on the deviation of the inverse average amplificationW⁻¹m(K) from 1. It has been found that the predistortion factor gPD(K)exhibits good convergence behavior during the adjustment process becauseof the correction value so formed. It applies for the adjustmentconstant Δ(K) that the smaller it is, the more slowly adjustment of thepredistortion factor gPD(K) occurs to a value that compensates for thenonlinearity of the amplifier VV. A slower adjustment process means thatit converges over several time intervals, which is equivalent to alonger lasting averaging process, so that disturbances, for example, bythermal noise, are better suppressed. Care must be taken for theadjustment process that the predistortion factor does not change toostrongly from one time interval to the next. It has therefore provenuseful to make the adjustment constant ΔK dependent on the number ofhits T(K) as stated in equation (12). As equation (13) makes clear forthe average amplification W(K), averaging of the amplification isstrongest for those quantization steps K for which the hit rateaccording to equation (12) is highest. It is useful to let theadjustment constant become greater, the stronger the averaging ofamplification W(K) or hit rate T(K) is for the individual quantizationsteps K. One possible stipulation for adjustment constant is shown inequation (15).

Δ(K)=min{0.01T(K); 0.5}  (15)

This equation (15) states that the adjustment constant Δ(K) is set equalto the smaller of the two values for the corresponding quantization stepK, in which the one value is 0.5 and the other value corresponds to onehundredth of the hit rate T(K) of the corresponding quantization step K.It is then assumed that roughly 10,000 scanning values pertain to onetime interval for which the average amplification W(K) and the hit rateT(K) are determined.

What is claimed is:
 1. A method of linearizing a high-frequencyamplifier, comprising the steps of: a) connecting a predistorter upline;b) adaptively altering a predistortion factor so that a linear relationexists between an output signal of the high-frequency amplifier and aninput signal of the predistorter; c) forming a quotient from the outputsignal of the high-frequency amplifier and the input signal of thepredistorter; d) determining an average amplification from the quotient;e) forming for the predistortion factor a correction term which dependson a deviation of the average amplification relative to a referencevalue; and f) continuing to adaptively alter the predistortion factor sothat the correction term becomes minimal.
 2. The method according toclaim 1, wherein the step of forming the correction term is formed froma product of an adjustment constant and a difference between an inverseof the average amplification and the numeral
 1. 3. The method accordingto claim 2, and the steps of forming a power quantity from the inputsignal of the predistorter, linearly quantizing the power quantity inquantization steps, allocating a value of the predistortion factor toeach quantization step, determining an average amplification for eachquantization step, and forming, for each predistortion factor allocatedto a respective said quantization step, a correction value dependent onthe average amplification determined in the corresponding quantizationstep, the correction value being minimized by adaptive alteration of thepredistortion factor.
 4. The method according to claim 3, wherein thestep of determining the average amplification in each quantization stepis performed by forming, over a specific time interval, amplificationvalues from time- and value-discrete scanning values of the outputsignal of the high-frequency amplifier and the input signal of thepredistorter, accumulating all amplification values corresponding to acorresponding quantization step, and dividing, for each quantizationstep, the amplification value resulting from accumulation at an end ofeach time interval by a number of accumulation steps.
 5. The methodaccording to claim 3, wherein the adjustment constant has a valuedependent on the corresponding quantization step to which thepredistortion factor is allocated.
 6. The method according to claim 5,wherein a smaller of the two values is chosen as the adjustmentconstant, in which one of the values has a value of 0.5, and in whichthe other of the values depends on the number of accumulations of theamplification values in the corresponding quantization step.